KILLED proof of input_YrFOYUvYOV.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 282 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 412 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 31 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (30) CdtProblem (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 84 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (204) 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, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) 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, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0') -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0') -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0') -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) 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, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (9) 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__isNatKind_1 a__and_2 a__isNat_1 a__U22_1 a__U11_3 a__U41_3 a__U31_2 a__U12_2 a__U21_2 a__U13_1 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) 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, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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, V2) -> a__U12(tt, V2) [2] a__U11(tt, plus(V1', V2'), V2) -> a__U12(a__U11(a__and(a__isNatKind(V1'), isNatKind(V2')), V1', V2'), V2) [2] a__U11(tt, s(V1''), V2) -> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) [2] a__U11(tt, V1, V2) -> a__U12(isNat(V1), V2) [2] a__U12(tt, 0) -> a__U13(tt) [2] a__U12(tt, plus(V11, V2'')) -> a__U13(a__U11(a__and(a__isNatKind(V11), isNatKind(V2'')), V11, V2'')) [2] a__U12(tt, s(V12)) -> a__U13(a__U21(a__isNatKind(V12), V12)) [2] a__U12(tt, V2) -> a__U13(isNat(V2)) [2] a__U13(tt) -> tt [1] a__U21(tt, 0) -> a__U22(tt) [2] a__U21(tt, plus(V13, V21)) -> a__U22(a__U11(a__and(a__isNatKind(V13), isNatKind(V21)), V13, V21)) [2] a__U21(tt, s(V14)) -> a__U22(a__U21(a__isNatKind(V14), V14)) [2] a__U21(tt, V1) -> a__U22(isNat(V1)) [2] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(0, V2)) -> a__U11(a__and(tt, isNatKind(V2)), 0, V2) [2] a__isNat(plus(plus(V15, V22), V2)) -> a__U11(a__and(a__and(a__isNatKind(V15), isNatKind(V22)), isNatKind(V2)), plus(V15, V22), V2) [2] a__isNat(plus(s(V16), V2)) -> a__U11(a__and(a__isNatKind(V16), isNatKind(V2)), s(V16), V2) [2] a__isNat(plus(V1, V2)) -> a__U11(a__and(isNatKind(V1), isNatKind(V2)), V1, V2) [2] a__isNat(s(0)) -> a__U21(tt, 0) [2] a__isNat(s(plus(V17, V23))) -> a__U21(a__and(a__isNatKind(V17), isNatKind(V23)), plus(V17, V23)) [2] a__isNat(s(s(V18))) -> a__U21(a__isNatKind(V18), s(V18)) [2] a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2] a__isNatKind(0) -> tt [1] a__isNatKind(plus(0, V2)) -> a__and(tt, isNatKind(V2)) [2] a__isNatKind(plus(plus(V19, V24), V2)) -> a__and(a__and(a__isNatKind(V19), isNatKind(V24)), isNatKind(V2)) [2] a__isNatKind(plus(s(V110), V2)) -> a__and(a__isNatKind(V110), isNatKind(V2)) [2] a__isNatKind(plus(V1, V2)) -> a__and(isNatKind(V1), isNatKind(V2)) [2] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(0, 0) -> a__U31(a__and(tt, isNatKind(0)), 0) [2] a__plus(plus(V111, V25), 0) -> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), isNatKind(V25)), V111, V25), isNatKind(plus(V111, V25))), plus(V111, V25)) [2] a__plus(s(V112), 0) -> a__U31(a__and(a__U21(a__isNatKind(V112), V112), isNatKind(s(V112))), s(V112)) [2] a__plus(N, 0) -> a__U31(a__and(isNat(N), isNatKind(N)), N) [2] a__plus(N, s(0)) -> a__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(N), isNatKind(N))), 0, N) [2] a__plus(N, s(plus(V113, V26))) -> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), isNatKind(V26)), V113, V26), isNatKind(plus(V113, V26))), and(isNat(N), isNatKind(N))), plus(V113, V26), N) [2] a__plus(N, s(s(V114))) -> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), isNatKind(s(V114))), and(isNat(N), isNatKind(N))), s(V114), N) [2] a__plus(N, s(M)) -> a__U41(a__and(a__and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [2] mark(U11(U11(X1104, X2104, X333), X2, X3)) -> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) [2] mark(U11(U12(X1105, X2105), X2, X3)) -> a__U11(a__U12(mark(X1105), X2105), X2, X3) [2] mark(U11(isNat(X100), X2, X3)) -> a__U11(a__isNat(X100), X2, X3) [2] mark(U11(U13(X101), X2, X3)) -> a__U11(a__U13(mark(X101)), X2, X3) [2] mark(U11(U21(X1106, X2106), X2, X3)) -> a__U11(a__U21(mark(X1106), X2106), X2, X3) [2] mark(U11(U22(X102), X2, X3)) -> a__U11(a__U22(mark(X102)), X2, X3) [2] mark(U11(U31(X1107, X2107), X2, X3)) -> a__U11(a__U31(mark(X1107), X2107), X2, X3) [2] mark(U11(U41(X1108, X2108, X334), X2, X3)) -> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) [2] mark(U11(plus(X1109, X2109), X2, X3)) -> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) [2] mark(U11(and(X1110, X2110), X2, X3)) -> a__U11(a__and(mark(X1110), X2110), X2, X3) [2] mark(U11(isNatKind(X103), X2, X3)) -> a__U11(a__isNatKind(X103), X2, X3) [2] mark(U11(tt, X2, X3)) -> a__U11(tt, X2, X3) [2] mark(U11(s(X104), X2, X3)) -> a__U11(s(mark(X104)), X2, X3) [2] mark(U11(0, X2, X3)) -> a__U11(0, X2, X3) [2] mark(U12(U11(X1111, X2111, X335), X2)) -> a__U12(a__U11(mark(X1111), X2111, X335), X2) [2] mark(U12(U12(X1112, X2112), X2)) -> a__U12(a__U12(mark(X1112), X2112), X2) [2] mark(U12(isNat(X105), X2)) -> a__U12(a__isNat(X105), X2) [2] mark(U12(U13(X106), X2)) -> a__U12(a__U13(mark(X106)), X2) [2] mark(U12(U21(X1113, X2113), X2)) -> a__U12(a__U21(mark(X1113), X2113), X2) [2] mark(U12(U22(X107), X2)) -> a__U12(a__U22(mark(X107)), X2) [2] mark(U12(U31(X1114, X2114), X2)) -> a__U12(a__U31(mark(X1114), X2114), X2) [2] mark(U12(U41(X1115, X2115, X336), X2)) -> a__U12(a__U41(mark(X1115), X2115, X336), X2) [2] mark(U12(plus(X1116, X2116), X2)) -> a__U12(a__plus(mark(X1116), mark(X2116)), X2) [2] mark(U12(and(X1117, X2117), X2)) -> a__U12(a__and(mark(X1117), X2117), X2) [2] mark(U12(isNatKind(X108), X2)) -> a__U12(a__isNatKind(X108), X2) [2] mark(U12(tt, X2)) -> a__U12(tt, X2) [2] mark(U12(s(X109), X2)) -> a__U12(s(mark(X109)), X2) [2] mark(U12(0, X2)) -> a__U12(0, X2) [2] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(U11(X1118, X2118, X337))) -> a__U13(a__U11(mark(X1118), X2118, X337)) [2] mark(U13(U12(X1119, X2119))) -> a__U13(a__U12(mark(X1119), X2119)) [2] mark(U13(isNat(X200))) -> a__U13(a__isNat(X200)) [2] mark(U13(U13(X201))) -> a__U13(a__U13(mark(X201))) [2] mark(U13(U21(X1120, X2120))) -> a__U13(a__U21(mark(X1120), X2120)) [2] mark(U13(U22(X202))) -> a__U13(a__U22(mark(X202))) [2] mark(U13(U31(X1121, X2121))) -> a__U13(a__U31(mark(X1121), X2121)) [2] mark(U13(U41(X1122, X2122, X338))) -> a__U13(a__U41(mark(X1122), X2122, X338)) [2] mark(U13(plus(X1123, X2123))) -> a__U13(a__plus(mark(X1123), mark(X2123))) [2] mark(U13(and(X1124, X2124))) -> a__U13(a__and(mark(X1124), X2124)) [2] mark(U13(isNatKind(X203))) -> a__U13(a__isNatKind(X203)) [2] mark(U13(tt)) -> a__U13(tt) [2] mark(U13(s(X204))) -> a__U13(s(mark(X204))) [2] mark(U13(0)) -> a__U13(0) [2] mark(U21(U11(X1125, X2125, X339), X2)) -> a__U21(a__U11(mark(X1125), X2125, X339), X2) [2] mark(U21(U12(X1126, X2126), X2)) -> a__U21(a__U12(mark(X1126), X2126), X2) [2] mark(U21(isNat(X205), X2)) -> a__U21(a__isNat(X205), X2) [2] mark(U21(U13(X206), X2)) -> a__U21(a__U13(mark(X206)), X2) [2] mark(U21(U21(X1127, X2127), X2)) -> a__U21(a__U21(mark(X1127), X2127), X2) [2] mark(U21(U22(X207), X2)) -> a__U21(a__U22(mark(X207)), X2) [2] mark(U21(U31(X1128, X2128), X2)) -> a__U21(a__U31(mark(X1128), X2128), X2) [2] mark(U21(U41(X1129, X2129, X340), X2)) -> a__U21(a__U41(mark(X1129), X2129, X340), X2) [2] mark(U21(plus(X1130, X2130), X2)) -> a__U21(a__plus(mark(X1130), mark(X2130)), X2) [2] mark(U21(and(X1131, X2131), X2)) -> a__U21(a__and(mark(X1131), X2131), X2) [2] mark(U21(isNatKind(X208), X2)) -> a__U21(a__isNatKind(X208), X2) [2] mark(U21(tt, X2)) -> a__U21(tt, X2) [2] mark(U21(s(X209), X2)) -> a__U21(s(mark(X209)), X2) [2] mark(U21(0, X2)) -> a__U21(0, X2) [2] mark(U22(U11(X1132, X2132, X341))) -> a__U22(a__U11(mark(X1132), X2132, X341)) [2] mark(U22(U12(X1133, X2133))) -> a__U22(a__U12(mark(X1133), X2133)) [2] mark(U22(isNat(X300))) -> a__U22(a__isNat(X300)) [2] mark(U22(U13(X301))) -> a__U22(a__U13(mark(X301))) [2] mark(U22(U21(X1134, X2134))) -> a__U22(a__U21(mark(X1134), X2134)) [2] mark(U22(U22(X302))) -> a__U22(a__U22(mark(X302))) [2] mark(U22(U31(X1135, X2135))) -> a__U22(a__U31(mark(X1135), X2135)) [2] mark(U22(U41(X1136, X2136, X342))) -> a__U22(a__U41(mark(X1136), X2136, X342)) [2] mark(U22(plus(X1137, X2137))) -> a__U22(a__plus(mark(X1137), mark(X2137))) [2] mark(U22(and(X1138, X2138))) -> a__U22(a__and(mark(X1138), X2138)) [2] mark(U22(isNatKind(X303))) -> a__U22(a__isNatKind(X303)) [2] mark(U22(tt)) -> a__U22(tt) [2] mark(U22(s(X304))) -> a__U22(s(mark(X304))) [2] mark(U22(0)) -> a__U22(0) [2] mark(U31(U11(X1139, X2139, X343), X2)) -> a__U31(a__U11(mark(X1139), X2139, X343), X2) [2] mark(U31(U12(X1140, X2140), X2)) -> a__U31(a__U12(mark(X1140), X2140), X2) [2] mark(U31(isNat(X305), X2)) -> a__U31(a__isNat(X305), X2) [2] mark(U31(U13(X306), X2)) -> a__U31(a__U13(mark(X306)), X2) [2] mark(U31(U21(X1141, X2141), X2)) -> a__U31(a__U21(mark(X1141), X2141), X2) [2] mark(U31(U22(X307), X2)) -> a__U31(a__U22(mark(X307)), X2) [2] mark(U31(U31(X1142, X2142), X2)) -> a__U31(a__U31(mark(X1142), X2142), X2) [2] mark(U31(U41(X1143, X2143, X344), X2)) -> a__U31(a__U41(mark(X1143), X2143, X344), X2) [2] mark(U31(plus(X1144, X2144), X2)) -> a__U31(a__plus(mark(X1144), mark(X2144)), X2) [2] mark(U31(and(X1145, X2145), X2)) -> a__U31(a__and(mark(X1145), X2145), X2) [2] mark(U31(isNatKind(X308), X2)) -> a__U31(a__isNatKind(X308), X2) [2] mark(U31(tt, X2)) -> a__U31(tt, X2) [2] mark(U31(s(X309), X2)) -> a__U31(s(mark(X309)), X2) [2] mark(U31(0, X2)) -> a__U31(0, X2) [2] mark(U41(U11(X1146, X2146, X345), X2, X3)) -> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) [2] mark(U41(U12(X1147, X2147), X2, X3)) -> a__U41(a__U12(mark(X1147), X2147), X2, X3) [2] mark(U41(isNat(X346), X2, X3)) -> a__U41(a__isNat(X346), X2, X3) [2] mark(U41(U13(X347), X2, X3)) -> a__U41(a__U13(mark(X347)), X2, X3) [2] mark(U41(U21(X1148, X2148), X2, X3)) -> a__U41(a__U21(mark(X1148), X2148), X2, X3) [2] mark(U41(U22(X348), X2, X3)) -> a__U41(a__U22(mark(X348)), X2, X3) [2] mark(U41(U31(X1149, X2149), X2, X3)) -> a__U41(a__U31(mark(X1149), X2149), X2, X3) [2] mark(U41(U41(X1150, X2150, X349), X2, X3)) -> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) [2] mark(U41(plus(X1151, X2151), X2, X3)) -> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) [2] mark(U41(and(X1152, X2152), X2, X3)) -> a__U41(a__and(mark(X1152), X2152), X2, X3) [2] mark(U41(isNatKind(X350), X2, X3)) -> a__U41(a__isNatKind(X350), X2, X3) [2] mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2] mark(U41(s(X351), X2, X3)) -> a__U41(s(mark(X351)), X2, X3) [2] mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(U11(X1258, X2258, X3116), X2)) -> a__and(a__U11(mark(X1258), X2258, X3116), X2) [2] mark(and(U12(X1259, X2259), X2)) -> a__and(a__U12(mark(X1259), X2259), X2) [2] mark(and(isNat(X441), X2)) -> a__and(a__isNat(X441), X2) [2] mark(and(U13(X442), X2)) -> a__and(a__U13(mark(X442)), X2) [2] mark(and(U21(X1260, X2260), X2)) -> a__and(a__U21(mark(X1260), X2260), X2) [2] mark(and(U22(X443), X2)) -> a__and(a__U22(mark(X443)), X2) [2] mark(and(U31(X1261, X2261), X2)) -> a__and(a__U31(mark(X1261), X2261), X2) [2] mark(and(U41(X1262, X2262, X3117), X2)) -> a__and(a__U41(mark(X1262), X2262, X3117), X2) [2] mark(and(plus(X1263, X2263), X2)) -> a__and(a__plus(mark(X1263), mark(X2263)), X2) [2] mark(and(and(X1264, X2264), X2)) -> a__and(a__and(mark(X1264), X2264), X2) [2] mark(and(isNatKind(X444), X2)) -> a__and(a__isNatKind(X444), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(s(X445), X2)) -> a__and(s(mark(X445)), X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (13) 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 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 2 }-> a__U13(1) :|: z = 1, z' = 0 a__U12(z, z') -{ 2 }-> a__U13(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 2 }-> a__U22(1) :|: z = 1, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + V1) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18) a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), 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__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 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 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 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(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300) mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301) mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U22(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202) mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201) mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U13(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (15) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 1 :|: z = 1 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U12(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 3 }-> 1 :|: V1 >= 0, z = 1, z' = V1, 1 + V1 = 1 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U21(z, z') -{ 3 }-> 1 + X :|: V1 >= 0, z = 1, z' = V1, X >= 0, 1 + V1 = X a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18) a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), 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__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 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 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 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(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300) mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301) mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202) mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201) mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z' - 1 >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), z'') :|: z = 1, z' = 1 + V1' + V2', z'' >= 0, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, z'') :|: z = 1, z'' >= 0, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U12(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z' - 1 >= 0, z = 1 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 3 }-> 1 :|: z' >= 0, z = 1, 1 + z' = 1 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U21(z, z') -{ 3 }-> 1 + X :|: z' >= 0, z = 1, X >= 0, 1 + z' = X a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__and(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (1 + (z' - 2))), 1 + (1 + z) + (1 + z)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + z) + (1 + z)), 1 + V113 + V26, z) :|: z' = 1 + (1 + V113 + V26), z >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z) + (1 + z)), 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + (z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + z, 1 + z), z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 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(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (21) 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 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 1 }-> a__U12(a__isNat(V1), V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 1 }-> a__U13(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 1 }-> a__U22(a__isNat(V1)) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 1 }-> a__U21(a__isNatKind(V1), V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__and(a__isNatKind(V1), 1 + V2), 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__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__and(a__isNatKind(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U41(a__and(a__and(a__isNat(M), 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U31(a__and(a__isNat(N), 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 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U13(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_2, A__U13_1, A__U21_2, A__U22_1, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13_2, c14, c15_1, c16, c17, c18_3, c19_2, c20, c21, c22_2, c23_1, c24, c25_3, c26_4, c27, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c40, c41_1, c42 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing nodes: A__PLUS(z0, z1) -> c27 A__U22(tt) -> c8 A__U12(z0, z1) -> c3 A__ISNATKIND(z0) -> c24 A__AND(z0, z1) -> c16 A__U31(z0, z1) -> c11 MARK(tt) -> c40 A__ISNATKIND(0) -> c21 A__U13(tt) -> c4 A__ISNAT(0) -> c17 A__U13(z0) -> c5 A__ISNAT(z0) -> c20 A__U21(z0, z1) -> c7 A__U11(z0, z1, z2) -> c1 MARK(0) -> c42 A__U41(z0, z1, z2) -> c14 A__U22(z0) -> c9 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_2, A__U21_2, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c2_2, c6_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2 Compound Symbols: c_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1 ---------------------------------------- (29) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) by A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) by A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) by A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) by MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) by MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) by MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) by MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) by A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) by A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) by A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, 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z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) by A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), 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c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) by A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) 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U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), 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c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> 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c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) 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a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) by A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) 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U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), 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x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), 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a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), 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z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), 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a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> 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c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) 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A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, 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c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), 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c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), 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A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), 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z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) by A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), 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0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> 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MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, 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c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), 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c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) 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isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) 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a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), 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x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) by A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> 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a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) by A__U41(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U41(tt, U12(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, isNat(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNat(z0)), MARK(U11(x1, x2, x3))) A__U41(tt, U13(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, U21(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, U22(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, U31(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, U41(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U41(tt, plus(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2, x3))) A__U41(tt, and(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, isNatKind(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U11(x1, x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, 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MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, 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c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), 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plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U12(x1, x2))) A__U41(tt, U12(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, isNat(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNat(z0)), MARK(U12(x1, x2))) A__U41(tt, U13(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U13(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, U21(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, U22(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U22(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, U31(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, U41(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U12(x1, x2))) A__U41(tt, plus(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U12(x1, x2))) A__U41(tt, and(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__and(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, isNatKind(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNatKind(z0)), MARK(U12(x1, x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, 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a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), 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mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by A__U41(tt, U11(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1, z2)), MARK(isNat(x1))) A__U41(tt, U12(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U12(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, isNat(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1))) A__U41(tt, U13(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U13(mark(z0))), MARK(isNat(x1))) A__U41(tt, U21(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, U22(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U22(mark(z0))), MARK(isNat(x1))) A__U41(tt, U31(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U31(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, U41(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1))) A__U41(tt, plus(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1))) A__U41(tt, and(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, isNatKind(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNatKind(z0)), MARK(isNat(x1))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), 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A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, 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a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) by A__U41(tt, U11(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U13(x1))) A__U41(tt, U12(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U12(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, isNat(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNat(z0)), MARK(U13(x1))) A__U41(tt, U13(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U13(mark(z0))), MARK(U13(x1))) A__U41(tt, U21(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U21(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, U22(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U22(mark(z0))), MARK(U13(x1))) A__U41(tt, U31(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U31(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, U41(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U13(x1))) A__U41(tt, plus(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U13(x1))) A__U41(tt, and(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__and(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, isNatKind(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNatKind(z0)), MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), 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plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> 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c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), 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c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U21(x1, x2))) A__U41(tt, U12(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, isNat(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNat(z0)), MARK(U21(x1, x2))) A__U41(tt, U13(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U13(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, U21(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, U22(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U22(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, U31(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, U41(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U21(x1, x2))) A__U41(tt, plus(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2))) A__U41(tt, and(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__and(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, isNatKind(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNatKind(z0)), MARK(U21(x1, x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> 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A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 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0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, 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c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) by A__U41(tt, U11(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U22(x1))) A__U41(tt, U12(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U12(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, isNat(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNat(z0)), MARK(U22(x1))) A__U41(tt, U13(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U13(mark(z0))), MARK(U22(x1))) A__U41(tt, U21(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U21(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, U22(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U22(mark(z0))), MARK(U22(x1))) A__U41(tt, U31(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U31(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, U41(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U22(x1))) A__U41(tt, plus(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U22(x1))) A__U41(tt, and(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__and(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, isNatKind(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNatKind(z0)), MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), 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c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> 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MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U41(tt, U12(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, isNat(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNat(z0)), MARK(U31(x1, x2))) A__U41(tt, U13(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U13(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, U21(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, U22(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U22(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, U31(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, U41(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U41(tt, plus(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U31(x1, x2))) A__U41(tt, and(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__and(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, isNatKind(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNatKind(z0)), MARK(U31(x1, x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), 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c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), 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A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), 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z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> 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MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), 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0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> 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MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, 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c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), 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A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by A__U41(tt, U11(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U41(tt, U12(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, isNat(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3))) A__U41(tt, U13(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, U21(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, U22(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, U31(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U41(tt, plus(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3))) A__U41(tt, and(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, isNatKind(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U41(x1, x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> 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z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, 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plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, 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MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, 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U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by A__U41(tt, U11(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U41(tt, U12(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, isNat(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2))) A__U41(tt, U13(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U13(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, U21(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, U22(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U22(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, U31(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, U41(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U41(tt, plus(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2))) A__U41(tt, and(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, isNatKind(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNatKind(z0)), MARK(plus(x1, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) 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A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), 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a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, 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mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> 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x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), 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x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), 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A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, 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c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, 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z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) by A__U41(tt, U11(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(and(x1, x2))) A__U41(tt, U12(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U12(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, isNat(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(and(x1, x2))) A__U41(tt, U13(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U13(mark(z0))), MARK(and(x1, x2))) A__U41(tt, U21(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, U22(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U22(mark(z0))), MARK(and(x1, x2))) A__U41(tt, U31(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U31(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, U41(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(and(x1, x2))) A__U41(tt, plus(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(and(x1, x2))) A__U41(tt, and(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, isNatKind(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNatKind(z0)), MARK(and(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), 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mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), 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c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> 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MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, 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U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> 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z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> 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A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) by A__U41(tt, U11(z0, z1, z2), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U11(mark(z0), z1, z2)), MARK(isNatKind(x1))) A__U41(tt, U12(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U12(mark(z0), z1)), MARK(isNatKind(x1))) A__U41(tt, isNat(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__isNat(z0)), MARK(isNatKind(x1))) A__U41(tt, U13(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U13(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, U21(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U21(mark(z0), z1)), MARK(isNatKind(x1))) A__U41(tt, U22(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U22(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, U31(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U31(mark(z0), z1)), MARK(isNatKind(x1))) A__U41(tt, U41(z0, z1, z2), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U41(mark(z0), z1, z2)), MARK(isNatKind(x1))) A__U41(tt, plus(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__plus(mark(z0), mark(z1))), MARK(isNatKind(x1))) A__U41(tt, and(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__and(mark(z0), z1)), MARK(isNatKind(x1))) A__U41(tt, isNatKind(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__isNatKind(z0)), MARK(isNatKind(x1))) A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1))) A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1))) A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0))) A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1)))) A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0)))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> 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c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> 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c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), 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0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1))) A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1))) A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0))) A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1)))) A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0)))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1))) A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1))) A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0))) A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1)))) A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0)))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), 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x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1))) A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0))) A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1)))) A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0)))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, tt, isNatKind(x1)) -> c12(MARK(isNatKind(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, 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MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), 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a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1))) A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1))) A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0))) A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1)))) A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0)))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, tt, isNatKind(x1)) -> c12(MARK(isNatKind(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2